U need a cutout as per your information originally it comes with one horn u installed 2 need more current
When your cars radiator fan is on it consume more current and doesn't give proper current to horn resulting no horn sound
As u said when the car cools down the radiator fan turns off the required current then goes to u horn and it honks
You solution is a cutout which gives extra current to horn and let it work properly
If u have already installed cutout then it might b faulty change it this might solve your problem
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